Proposal for a 'peculiar' double-slit experiment

[Dionysus]

Hi to all who might respond,

Consider the 'peculiar' double-slit setup below.
There is a double-slit configuration such that the two slits are never open at the same time. That is: whenever the top slit is open for a certain interval, Ts, the bottom slit is closed for the same interval and vice versa; the configuration toggles continuously between these two states. Lets assume that we have a pulsed sub-single-photon source whose broad-band pulse coherence time, Tp, is much less than Ts. The source targets the double-slit in the following manner: it splits each pulse (which contains at most one photon) into two time bins, synchronized with the opening/closing of the slits, separated by an interval Ts, such that the first time-bin pulse passes at the half-time of when the top slit is open while the second time-bin pulse passes at the half-time of when the bottom slit is open. Thus, a photon never experiences both slits open. Suppose that, just before the detection screen, we place a narrow-band spectral filter such that the coherence time of photons that pass the filter, Tf, is much larger than the slit toggling interval Ts.......Will we see an interference pattern, since now it is impossible, even in principle, to determine through which slit a photon passed? Does this gedanken experiment have any implications (positive or negative) pertaining to the 'Standard' or the 'Bohmian' interpretations of QM?
Demetrios

 

[Enthalpy]

Hi Dionysus, hope to have grasped the description properly.

The photon has a short coherence time and is split in two intervals. I will add the hypothesis that the two intervals are a bit separated, so that the wave isn't correlated in the two intervals. This avoids the intermediate cases as the end of the first interval is slightly correlated with the beginning of the second one.

Whether you open and close the slits or not has no influence. The source that splits the pulse in two and directs the halves at different slits has already done that job.

Whether you have one or several photons makes no difference.

When recombining the two intervals, you get no interference, because they are not coherent.

The narrow-band filter doesn't change that. It loses power of the wideband light, makes the half-pulses longer so that they now overlap, but their superposition will not be consistently additive at some constant places and subtractive at others, because their relative phase changes randomly, after the filter too.

----------

As opposed, you can make interferences with slits open at different times, provided that you delay the wave passed through the earlier slit. It would also work with the narrow-band filter and no delay, but needs a source with a coherence time that spans the two intervals.

----------

In such photon experiments, single or multiple photons use to make no difference. You can propagate photons like a non-quantized wave, and only upon detection and if needed, remember that some properties don't split.